Algebra
С открытой датой
Описание мероприятия
Язык обучения: английскийОписание программы
This unit develops a student’s proficiency in working with the mathematical methods of algebra and develops the student’s understanding of the theoretical concepts (such as vector space) behind these methods
The objectives specifically include:
- to enable students to acquire skills in the methods of algebra, as required for their use in further mathematics subjects and economics-based subjects
- to prepare students for further units in mathematics and/or related disciplines
Assessment
This course is assessed by a three-hourunseen written examination.
Учебный план:
Matrices, vectors and their geometry: Vectors and matrices, the algebra of vectors and matrices; Cartesian and vector equations of a straight line; normal vectors and planes; the Cartesian and vector equations of a plane; extension to higher dimension.
Systems of linear equations: Systems of linear equations and their expression in matrix form; Solving systems of linear equations using row operations; consistent and inconsistent systems; systems with free variables; range and rank of a matrix; general solution of linear systems.
Matrix inversion and determinants: finding inverses using row operations; determinants; matrix inversion using cofactors; Cramer’s rule; input-output analysis.
Sequences, series and difference equations: Arithmetic and Geometric Progressions; sums of numbers, squares and cubes; solving firstorder difference equations; application of first-order difference equations to financial problems; the cobweb model; Second-order difference equations.
Vector spaces and related concepts: Vector spaces; subspaces, including those associated with matrices; linear span; linear independence and dependence; bases and dimension; coordinates; linear transformations.
Diagonalisation of matrices: eigenvalues and eigenvectors; diagonalisation of a matrix and its connection with eigenvectors; finding powers of matrices using diagonalisation;
Applications of diagonalisation: Markov chains; using diagonalisation to solve systems of differential equations
Результат обучения:
At the end of the course and having completed the essential reading and activities students should be able to:
- use the concepts, terminology, methods and conventions covered in the unit to solve mathematical problems in this subject
- solve unseen mathematical problems involving understanding of these concepts and application of these methods
- see how algebra can be used to solve problems in economics and related subjects
- demonstrate knowledge and understanding of the underlying principles of algebra.
Требования к поступающим:
The course may not be taken with MT105b Mathematics 2